*Article* **Thermal–Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning**

**Xiangsheng Lei 1 , Jinwu Ouyang 2 , Yanfeng Wang 1 , Xinghua Wang 1 , Xiaofeng Zhang 3 , Feng Chen 3 , Chang Xia 2 , Zhen Liu 2,\* and Cuiying Zhou 2, \***


**Abstract:** The panel performance of a prefabricated cabin-type substation under the impact of fires plays a vital role in the normal operation of the substation. However, current evaluations of the panel performance of substations under fire still focus on fire resistance tests, which seldom consider the relationship between fire behavior and the mechanical load of the panel under the impact of fires. Aiming at the complex and uncertain relationship between the thermal and mechanical performance of the substation panel under impact of fires, this paper proposes a machine learning method based on a BP neural network. First, the fire resistance test and the stress test of the panel is carried out, then a machine learning model is established based on the BP neural network. According to the collected data, the model parameters are obtained through a series of training and verification processes. Meanwhile, the correlation between the panel performance and fire resistance was obtained. Finally, related parameters are input into the thermal–mechanical coupling evaluation model for the substation panel performance to evaluate the fire resistance performance of the substation panel. To verify the correctness of the established model, numerical simulation of the fire test and stress test of the panel is conducted, and numerical simulation samples are predicted by the trained model. The results show that the prediction curve of neural network is closer to the real results compared with the numerical simulation, and the established model can accurately evaluate the thermal–mechanical coupling performance of the substation panel under fire.

**Keywords:** prefabricated cabin-type substation; panel; BP neural network; thermal–mechanical coupling; machine learning; fire behavior; impact of fires

#### **1. Introduction**

With the development of the national economy, the demand for electricity, from all walks of life, has increased. After a period of rapid development, large-scale centralized new energy power generation has gradually extended in the direction of decentralization and miniaturization. The requirements of new energy construction cannot be met by conventional transmission substations. Technological development and the improvement of prefabricated substations have become increasingly prominent. As a new type of prefabricated substation [1–3], the prefabricated cabin-type substation is becoming an important development direction benefiting from its high degree of integration and high level of intensiveness. Fire has an important effect on the safety of buildings and structures [4,5], thus the performance of the prefabricated substation panel under impact of fires is a guarantee of safety and plays a vital role in the normal operation of the substation. As

**Citation:** Lei, X.; Ouyang, J.; Wang, Y.; Wang, X.; Zhang, X.; Chen, F.; Xia, C.; Liu, Z.; Zhou, C. Thermal– Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning. *Fire* **2021**, *4*, 93. https://doi.org/ 10.3390/fire4040093

Academic Editor: Maged Youssef

Received: 15 November 2021 Accepted: 7 December 2021 Published: 9 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

a structural stress component of the substation panel, at the beginning of the design, the fire safety of the panel needs to be considered to ensure the safety of the overall structure of the substation. A high temperature causes the deterioration of the mechanical properties of the substation panel material, which will bring about different degrees of damage to the substation panel. Therefore, before the construction of the substation, it is necessary to carry out a fire resistance performance test under fire on the panel to ensure the fire resistance safety of the entire project in the event of a fire. Therefore, accurately describing the fire performance of substation panels has become an important issue for the stability of current substations.

Since the substation panels are mainly reinforced concrete structures, the fire performance of the substation panels can refer to the fire resistance test [6–10] and numerical simulation method to analyze fire behavior. Naser and Kodur [11] conducted an experimental study on the fire behavior of composite steel girders subjected to high shear loading. Hawileh et al. [12–14] predicted the performance of concrete beams using a finite element model. Aguado et al. [15] used a 3D finite element model for predicting the fire behavior of hollow-core slabs. However, the current research on the performance of substation panels rarely considers correlations, with little consideration of the nonlinear relationship between stress performance and fire resistance under impact of fire.

The neural network, a method of machine learning, is widely used in various fields [16–23]. Abuodeh et al. [24,25] used machine learning techniques to predict behavior of RC beams and compressive strength of ultra-high-performance concrete. Liu et al. [26] established machinelearning-based models to predict shear transfer strength of concrete joints. The neural network also has a precedent in the application of substation [27–31]. Da Silva et al. [32] proposed the use of artificial neural networks to solve the problem of fault location in substations; Wang et al. [33] used deep learning methods to identify the switch status of substations; Jiang Hongyu et al. [34] proposed an adaptive suppression method of transformer noise in substations based on genetic wavelet neural networks for the problem of transformer noise control; Oliveira et al. [35] carried out automatic monitoring on the construction site of substations based on deep learning. Neural networks [36–38] with selflearning, self-organization, and extremely strong linear fidelity capabilities can accurately reflect the nonlinear relationship between input and output variables to maintain high accuracy in short-term prediction. Therefore, machine learning is used to establish a non-linear relationship between panel stress and fire resistance from the perspective of thermal–mechanical coupling, which is a worthwhile means for evaluating the performance of substation panels under impact of fire.

To solve the above problem, this paper proposes a machine learning method based on the principle of BP (back propagation) neural networks to analyze the thermal–mechanical coupling performance of substation panels under fire. The evaluation factors are selected, such as the substation panel geometric data, mechanical performance parameters, and fire resistance performance data. After the model training ends, the relationship between panel mechanical performance and fire resistance is established. Finally, predictive samples are input into the model to evaluate the fire resistance performance of the panel. Then, fire resistance test and the stress test of the panel is carried out. A BP neural network model is trained and built through a series of training the samples. Then, numerical simulation of the fire test and stress test of the panel is conducted, and numerical simulation samples is predicted by the trained model and compared with the real results. The results show that predicted samples fit well with the actual output values and better than the result of numerical simulation. Thus, the established model can accurately evaluate the thermal– mechanical coupling performance of the panel under fire.

#### **2. Research Methods and Contents**

*2.1. The Research Process for Thermal–Mechanical Coupling Evaluation of Prefabricated Cabin-Type Substation Panel Performance*

The key to the thermal–mechanical coupling evaluation process of a prefabricated substation panel is to establish an evaluation model based on BP neural networks. By

inputting the stress state data of the substation panel into the evaluation model, the corresponding fire resistance parameters can be obtained. The thermal–mechanical coupling performance of the prefabricated substation panel can then be evaluated. The research process of the thermal–mechanical coupling evaluation of prefabricated substation panel performance is shown in Figure 1.

**Figure 1.** Research process of thermal–mechanical coupling evaluation of panel performance.

*2.2. Thermal–Mechanical Coupling Evaluation Model of the Panel Performance Based on BP Neural Networks*

#### 2.2.1. Establishment of Evaluation Factors

In theory, the performance state of the prefabricated substation panel can be better described by the more comprehensive evaluation indexes. However, in practical engineering, on the one hand, it is very difficult to collect data. On the other hand, the more indexes there are, the more complex the nonlinear relationship of the thermal–mechanical coupling evaluation of the prefabricated substation panel performance is. Therefore, the determination of evaluation indexes cannot be simply generalized but should be analyzed in specific cases. As a complex system, the thermal–mechanical coupling evaluation of panel performance is affected by many factors. This study, adhering to the principles of representativeness, integrity, and desirability, takes the geometric parameters, mechanical performance, and fire resistance performance of the panel as evaluation factors of the thermal–mechanical coupling evaluation of the panel's performance.


#### 2.2.2. Construction of BP Neural Network

The BP neural network as a method of machine learning is suitable for addressing complex nonlinear problems, such as the nonlinear relationship between the mechanical performance and the fire resistance performance of substation panels. The research process of the BP neural network model for the thermal–mechanical coupling evaluation of substation panel performance is shown in Figure 2. Firstly, the data parameters are input into the BP neural network for training. Secondly, the thermal–mechanical coupling evaluation results of the panel performance can be obtained through the model after model training. After that, we carried out numerical simulation of fire resistance test and stress test on the panel. We used the curve data of numerical simulation as sample data to predict the sample of numerical simulation. Finally, the correctness of the model is verified by comparing the real results with the numerical simulation results and the neural network prediction results.

a ω *θ* **Figure 2.** Research process of the BP neural network model in the thermal–mechanical coupling evaluation of prefabricated substation panel performance. *x*<sup>1</sup> , *x*<sup>2</sup> , . . . , *x*<sup>5</sup> , respectively, represents input layer parameters of neural network; *u*<sup>1</sup> , *u*<sup>2</sup> , . . . , *u<sup>k</sup>* represent hidden layer parameters of the neural network, respectively; *y<sup>j</sup>* represents output layer parameters of neural network; *N<sup>i</sup>* represents output results of neural network; ω represents weights of neural network and *θ* represents thresholds of neural network.

As shown in Figure 3, the BP neural network used for the thermal–mechanical coupling evaluation training of the prefabricated cabin-type substation panel performance is composed of three layers, representing the input layer, hidden layer, and output layer, respectively.

The input layer has seven impact indicators corresponding to the identification indicators, which are the length, width, height, heating time, average furnace temperature, average temperature, and pressure of the backfire surface. The output layer represents time and bending load. Therefore, there are seven input layer nodes in this model, six hidden layer nodes, and two output nodes. Each node is a specific output function, and each connection between two nodes represents a weighted value (weight) for the signal passing through the connection. The learning rate determines the amount of weight change generated in each cycle. The fixed learning rate in this research is 0.1, the training target is 0.00001, and the maximum number of learning iterations is 100. Through repeated iterative calculations, the correlation coefficient and threshold are determined. After that, the learning and training process ends, which means the model is successfully established. After the BP neural network model training, the actual value is compared with the predicted value. In order to solve the problem of inconsistency in the units and magnitudes of the input variables in the BP neural network, normalization is used to control the sample data to 0–1.

**Figure 3.** Application of the BP neural network in the thermal–mechanical coupling evaluation of substation panel performance.

The normalization formula is as follows:

$$Y\_{\bar{i}} = \frac{X\_{\bar{i}} - X\_{\text{min}}}{X\_{\bar{i}} - X\_{\text{max}}} \alpha + \beta \tag{1}$$

In the formula, *X<sup>i</sup>* and *Y<sup>i</sup>* represent the variables before and after normalization, respectively; *Xmin* and *Xmax* are the minimum and maximum values of *X<sup>i</sup>* , respectively; *α* is a parameter with a value between 0–1, and *<sup>β</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> *<sup>α</sup>* 2 .

#### **3. Case Application Analysis**

#### *3.1. Substation Panel*

3.1.1. Fire Resistance Test of Panel

The fire resistance test of panel refer to the requirements of GB/T 9978.1-2008 "Fire resistance Test Methods for Building Components part 1: General Requirements [39]" and GB/T 9978.8-2008 "Fire resistance Test Methods for Building Components Part 8: Characteristics of non-load-bearing vertical dividers [40]", as shown in Table 1. The test conditions and test plan were formulated according to the requirements of GB/T 9978.1- 2008 [39] and GB/T 9978.8-2008 [40].

 = − − ௫ + The length (m) width (m) × height (m) of the special panel for a box-type substation is 2.0 × 1.0 × 0.12. Ten temperature measurement points are set on the backfire surface of the panel with the vertical side on a free side, as shown in Figure 4.

 ௫ =1− <sup>ఈ</sup> ଶ According to the test requirements, the test uses vertical component fire test furnace device in Beijing Gequ fire test laboratory. The device can meet the requirements of the furnace temperature and pressure in Table 1. This device also can measure the temperature and pressure change value of the panel specimen. The data changes during the test can be visually displayed on the display screen of the equipment.


**Table 1.** Reference standards for fire resistance.

The experiment was terminated at 181 min. The test process was observed and recorded. The test phenomena are shown in Table 2.



The fire resistance data of the panels are shown in Figures 5 and 6.

**Figure 5.** Temperature rise curve.

3.1.2. The Stress Test of the Panel

The same panel specimen as Section 3.1.1 was used in this experiment. Static loading is carried out by force control. A hydraulic jack was used for loading. During the test, the load is acted on the mid-span position of the panel through the actuating head. Once the specimen was destroyed, the test was over. The data of the stress test of the panel are shown in Figure 7.

**Figure 6.** Pressure curve at 500 mm below the furnace roof.

**Figure 7.** Stress curve of the panel strength test. Bending load refer to a load that causes bending deformation of a panel during a fixed strength test.

#### *3.2. Thermal–Mechanical Coupling Evaluation of Panel Performance*

The values were recorded every minute from the origin of the coordinates. Figures 5 and 6 show that the test specimen was damaged when heated to the 183rd minute. Figure 7 shows that the test specimen was damaged under stress at 329.052 s. The time from loading to failure was divided into 183 segments for the values recorded every 1.798 s. The fire resistance and stress performance data of the panel are shown in Appendix A. It should be emphasized that the temperature measured in Table A1 has subtract the ambient temperature. The data of columns 1 represent the number of samples; the data of columns 2 represent the heating time of panel; the data of columns 6 represent the load time of the panel.

According to the BP neural network structure constructed in Section 2.2, the thermal– mechanical coupling evaluation model of the panel performance was learned and trained:

t


**Figure 8.** Comparison of sample predicted output and actual output.

It can be seen from Figure 8 that the predicted output values of the 84 groups of predicted samples fit well with the actual output values for the trend of the sample points showing basically the same, which indicates that the thermal–mechanical coupling evaluation model of panel performance based on a BP neural network is reasonable and accurate.

The mechanical performance data of the panel corresponding to the heating time of the 162nd minute to the 183rd minute were collected, as shown in Figure 9.

It can be seen from Figure 9 that, when the test specimen reaches the maximum bending load of 21.443 KN, the corresponding stress time of the substation plate is 294.888 s. When the time is 325.456 s, the bending load drops sharply from 18.664 KN, which means the material is damaged at this time. The prediction sample data of the fire resistance performance of the substation are input into the thermal–mechanical coupling evaluation model of the panel performance. The corresponding panel performance parameters can then be obtained. The test specimen reaches the maximum bending load of 21.128 KN when the predicted value of the neural network is displayed for 297.147 s. The bending load drops sharply from 18.683 KN for the material being damaged at the time of 323.658 s. By comparing the predicted value and actual value of the time and bending load, it is found that the maximum bending load and the corresponding stress time from the thermal– mechanical coupling evaluation model and actual test is very close, and the two values

essentially satisfy the error requirements. This further demonstrates the accuracy and reliability of the thermal–mechanical coupling evaluation model of the panel performance.

**Figure 9.** Sample result output of panel performance prediction.

#### *3.3. Numerical Simulation*

In order to verify the results of neural network calculation, we carried out numerical simulation on the specimen. The length (m) × width (m) × height (m) of the special panel for numerical simulation is 2.0 × 1.0 × 0.12, as shown in Figure 10. The fire resistance test and pressure test of numerical simulation model are consistent with the actual situation in Section 3.1. .

**Figure 10.** Numerical simulation model.

The numerical simulation results are shown in Figures 11 and 12.

**Figure 11.** Numerical simulation of fire resistance test.

.

**Figure 12.** Numerical simulation of stress test.

. The curve of the fire resistance test and pressure test parameters for the panel is shown in Figures 13 and 14. Each step in the diagram represents a unit of time. .

**Figure 13.** The curve of the fire resistance test.

**Figure 14.** Stress curve of the panel samples. Bending load refer to a load that causes bending deformation of a panel during a fixed strength test.

.

The failure time step of numerical simulation corresponds to the failure time of fire resistance test and pressure test in real time, and the simulated result curve is also divided into 183 sections. Corresponding values are recorded in each section and 184 sample data of numerical simulation can be obtained. trained

According to the BP neural network structure trained in Section 3.2, we conduct neural network learning, training and prediction using the sample data of numerical simulation. According to the sample data of numerical simulation, the prediction results of numerical simulation are obtained. By converting the failure time of the real stress curve into the corresponding time step, we plotted the prediction curve of the neural network, the prediction curve of the numerical simulation and the real stress test curve in the same figure, as shown in Figure 15. . 15.

**Figure 15.** The stress test curve.

m Figure 15 t It can be seen from Figure 15 that the curve of prediction result of neural network and array simulation is basically consistent with the curve of real pressure test. The force increases gradually and decreases rapidly after reaching the peak value. Numerical simulation results show that when the time step is 15,850, the maximum bending load

is 18.11064 kN. The neural network prediction results show that when the time step is 14,687, the bending load reaches the maximum value of 19.963 KN. The actual test results show that when the time step is 15,889, the bending load reaches the maximum value of 21.443 kN. Compared with the results of numerical simulation, the prediction curve of neural network is closer to the real pressure curve. The percentage error of the maximum bending load calculated by numerical simulation is 15.5%, the percentage error of the maximum bending load calculated by neural network prediction is 6.9%, and the error of neural network prediction is about half smaller than that of numerical simulation. The prediction result of neural network is better than that of numerical simulation. Thus, the accuracy and rationality of the neural network prediction model can be proved.

#### *3.4. The Functional Relationship between Fire Resistance and Stress Resistance*

The relationship between the parameters of fire resistance and stress resistance can be obtained by deriving the training parameters of the neural network, as shown in Equations (2)–(5):

$$\alpha\_{\rm h} = \sum\_{i=1}^{M} v\_{i\rm h} x\_i + r\_{\rm h} \tag{2}$$

$$b\_h = f(\mathfrak{a}\_h) \tag{3}$$

$$w\_{j} = \sum\_{h=1}^{q} w\_{hj} b\_{h} + \theta\_{j} \tag{4}$$

$$f(\mathbf{x}) = \frac{1}{1 + e^{-\mathbf{x}}} \tag{5}$$

*M* refers to the number of nodes in the input layer, *M* = 7; *x<sup>i</sup>* (*i* = 1, 2, . . . . . . , M) refers to length (m), width (m), height (m), heating time (min), average furnace temperature ( ◦C), average temperature of backfire surface (◦C), and pressure parameter (Pa); *h* refers to the number of hidden layer nodes, *h* = 6; *q* is the number of nodes in the output layer, *q* = 2; *y<sup>j</sup>* (*j* = 1, 2) refers to the values of the time (s) and bending load (KPa), respectively. *v* refers to weight parameters from input layer to hidden layer of neural network; *r<sup>h</sup>* refers to threshold parameters from input layer to hidden layer of neural network; *W* refers to weight parameters from hidden layer to output layer of neural network; *θ<sup>j</sup>* refers to threshold parameters from hidden layer to output layer of neural network.

$$v = \begin{bmatrix} 0 & 0 & 0 & 4.4136 & -1.6295 & -0.0460 & -0.1070 \\ 0 & 0 & 0 & 0.8386 & -0.7978 & -2.0962 & 0.1305 \\ 0 & 0 & 0 & -1.4522 & -1.0707 & -0.3682 & -0.0326 \\ 0 & 0 & 0 & 0.1633 & -0.3356 & -0.6002 & -0.0347 \\ 0 & 0 & 0 & 1.0436 & -0.0877 & -0.4381 & -0.0416 \\ 0 & 0 & 0 & 1.1642 & -0.2854 & -0.3663 & 0.1397 \end{bmatrix}$$

$$r\_h = \begin{bmatrix} -3.3526 & -1.0328 & -0.2724 & 0.6572 & -0.1576 & 0.9250 & \end{bmatrix}^{\mathrm{T}}$$

$$\theta\_j = \begin{bmatrix} 0.0798 & -0.1080 & -0.0044 & -0.7329 & 0.9450 & 0.2738 \\ -1.4042 & 0.0712 & -0.6059 & -0.4502 & 0.7257 & 0.0036 \end{bmatrix}$$

#### **4. Conclusions**

Based on the evaluation factors such as the geometric data of the substation panel, the stress performance, the fire resistance performance data, etc., a BP neural network, a method of machine learning, was used to establish the nonlinear relationship between panel performance stress and fire resistance under impact of fire. This model can quickly predict the performance of the substation panel under fire. The prediction of the thermal– mechanical coupling evaluation model is very close to the actual test, and satisfy the error

requirements. Additionally, the specimen was verified by numerical simulation. Comparing the neural network with numerical simulation, the result indicates the error of neural network prediction is about half smaller than that of numerical simulation, the prediction result of neural network is better than that of numerical simulation. The correctness and reliability of the thermal–mechanical coupling performance evaluation model is verified. If meeting the requirements of the test itself and the amount of data required by the structure of the neural network, the thermal–mechanical coupling evaluation model constructed in this study can be directly used for similar models. It does not need to conduct additional tests. As the types and quantities of data for training become richer, the models we build will become more and more refined. Therefore, this can provide a reference for exploring more thermal coupling evaluation models and complex functional relationships of materials based on neural networks under different loading modes in the future.

**Author Contributions:** Conceptualization, methodology, data curation, formal analysis; writing review and editing, project administration, funding acquisition, Z.L.; conceptualization, methodology, supervision, project administration, funding acquisition, C.Z.; data curation, formal analysis, writing original draft, preparation and editing, J.O.; data Curation, X.L.; data curation, Y.W.; data curation, X.W.; data curation, X.Z.; data curation, F.C.; data Curation, C.X., J.O. and X.L. contributed equally to this work and they are co-first authors of this article. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Science and Technology Project of Guangdong Power Grid Co., Ltd (037700KK52190022), the National Natural Science Foundation of China (NSFC) (Grant No.41977230), the National Key Research and Development Project (Grant No. 2017YFC1501203, No. 2017YFC1501201), the Special Fund Key Project of Applied Science and Technology Research and Development in Guangdong (Grant No. 2015B090925016, No. 2016B010124007).

**Institutional Review Board Statement:** The study did not require ethical approval.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank the anonymous reviewers for their very constructive and helpful comments.

**Conflicts of Interest:** The authors declare that they have no conflict of interest.

#### **Appendix A**

**Table A1.** Fire resistance and stress performance data of the panel.



**Table A1.** *Cont*.


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Table A1. Cont.
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**Table A1.** *Cont*.


**Table A1.** *Cont*.


**Table A1.** *Cont*.

#### **References**


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